A computer model is used to study the radiative transfer of the martian winter-polar atmosphere. Solar heating at winter-polar latitudes is provided predominately by dust. For normal, low-dust conditions, CO2 provides almost as much heating as dust. Most heating by CO2 in the winter polar atmosphere is provided by the 2.7 micron band between 10 km and 30 km altitude, and by the 2.0 micron band below 10 km. The weak 1.3 micron band provides some significant heating near the surface. The minor CO2 bands at 1.4, 1.6, 4.8 and 5.2 micron are all optically thin, and produce negligible heating. O3 provides less than 10 percent of the total heating. Atmospheric cooling is predominantly thermal emission by dust, although CO2 15 micron band emission is important above 20 km altitude.